Certification Problem

Input (TPDB SRS_Standard/Trafo_06/dup17)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

1.1 Reduction Pair Processor

1.1.1 Monotonic Reduction Pair Processor

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  b#(b(a(a(x1))))	→	a#(a(b(b(x1))))	(8)
  a#(a(a(a(x1))))	→	b#(b(x1))	(6)

  1.1.1.1.1 Reduction Pair Processor

  Using the linear polynomial interpretation over the naturals

  [b#(x1)]	=	1 · x1
  [b(x1)]	=	1 · x1
  [a(x1)]	=	1 + 1 · x1
  [a#(x1)]	=	1 + 1 · x1
  [c(x1)]	=	0

  the pair

  a#(a(a(a(x1))))

  →

  b#(b(x1))

  (6)

  could be deleted.

  1.1.1.1.1.1 Reduction Pair Processor with Usable Rules

  Using the linear polynomial interpretation over the naturals

  [b#(x1)]	=	1 + 1 · x1
  [b(x1)]	=	0
  [a(x1)]	=	0
  [a#(x1)]	=	0
  [c(x1)]	=	0

  having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair

  b#(b(a(a(x1))))

  →

  a#(a(b(b(x1))))

  (8)

  could be deleted.

  1.1.1.1.1.1.1 P is empty

  There are no pairs anymore.